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Tessellation from Rectangle by abbey

Tessellation from Rectangle by abbey
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2013-07-12 06:20
PolygonVectorGeometric Construction
In collections Tessellation from Rectangle using Translation
This example demonstrates how to generate a tessellation pattern using a rectangle. Key mathematical concepts include geometric construction and transformation. Using commands such as Segment, OrthogonalLine, Point, Intersect, Vector, Translate, Polygon, and Circle, complex tessellation patterns can be constructed. Suitable for middle school and above students to learn geometric transformations and tessellation construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Segment(C, A) → e
  8. Segment(D, B) → f
  9. Segment(C, D) → g
  10. Segment(A, E) → h
  11. Segment(E, F) → i
  12. Segment(F, G) → j
  13. Segment(G, H) → k
  14. Segment(H, C) → l
  15. Vector(C, D) → u
  16. Translate(C, u) → C'
  17. Translate(A, u) → A'
  18. Segment(C', A') → e'
  19. Translate(A, u) → A'_1
  20. Translate(E, u) → E'
  21. Segment(A'_1, E') → h'
  22. Translate(E, u) → E'_1
  23. Translate(F, u) → F'
  24. Segment(E'_1, F') → i'
  25. Translate(F, u) → F'_1
  26. Translate(G, u) → G'
  27. Segment(F'_1, G') → j'
  28. Translate(G, u) → G'_1
  29. Translate(H, u) → H'
  30. Segment(G'_1, H') → k'
  31. Translate(H, u) → H'_1
  32. Translate(C, u) → C'_1
  33. Segment(H'_1, C'_1) → l'
  34. Segment(A, I) → m
  35. Segment(I, J) → n
  36. Segment(J, K) → p
  37. Segment(K, L) → q
  38. Segment(L, M) → r
  39. Segment(M, B) → s
  40. Vector(A, C) → v
  41. Translate(A, v) → A'_2
  42. Translate(B, v) → B'
  43. Segment(A'_2, B') → a'
  44. Translate(A, v) → A'_3
  45. Translate(I, v) → I'
  46. Segment(A'_3, I') → m'
  47. Translate(I, v) → I'_1
  48. Translate(J, v) → J'
  49. Segment(I'_1, J') → n'
  50. Translate(J, v) → J'_1
  51. Translate(K, v) → K'
  52. Segment(J'_1, K') → p'
  53. Translate(K, v) → K'_1
  54. Translate(L, v) → L'
  55. Segment(K'_1, L') → q'
  56. Translate(L, v) → L'_1
  57. Translate(M, v) → M'
  58. Segment(L'_1, M') → r'
  59. Translate(M, v) → M'_1
  60. Translate(B, v) → B'_1
  61. Segment(M'_1, B'_1) → s'
  62. Translate(A', v) → A''
  63. Translate(A'_1, v) → O
  64. Polygon(C, H, M, B, E', F', G', H', D, M', L', K', G, J', I', F, E, A, I, J, K, L) → poly1, c_1, l_1, m_1, b_1, e'_1, f', g', h'_1, d_1, m'_1, l'_1, h_1, k'_1, j'_1, i'_1, g_1, f_1, e_1, a_1, i_1, j_1, k_1
  65. Point(i) → P
  66. Circle(N, P) → t
  67. Point(j) → R
  68. Circle(Q, R) → p_1